Average Cost. A company manufacturing snowboards has fixed costs of $200 per day and total costs of $3800 per day for a daily output of 20 boards.

Assuming that the total cost per day C(x) is linearly related to the total output per day x, write an equation for the cost function.

Final answer:

To solve the equation ky - bf = fy/m, you need to isolate the variable y. The steps are to distribute the k, add kf to both sides, and factor out y. The solution is y = (fy/m + kf)/k.

Explanation:

To solve the equation ky - bf = fy/m, we first want to isolate the variable y. Here are the steps:

Distribute the k to both terms in the equation: ky - bf = fy/m becomes ky - kf = fy/m.

Add kf to both sides of the equation: ky - kf + kf = fy/m + kf simplifies to ky = fy/m + kf.

Factor out y on the left side of the equation: y(k) = fy/m + kf becomes y = (fy/m + kf)/k.

So, the solution is y = (fy/m + kf)/k.

Answer:

Rotations, reflections, and translations are isometric. That means that these transformations do not change the size of the figure. If the size and shape of the figure is not changed, then the figures are congruent.

Step-by-step explanation:

Final answer:

The integer 27 can be written as the product of the perfect square 9 and the integer 3, expressed as 9 x 3.

Explanation:

To write the integer 27 as a product of two integers such that one of the factors is a perfect square, we can break down 27 into its prime factors. The prime factorization of 27 is 3 x 3 x 3, which can be written as 9 x 3 because 9 is a perfect square (3 x 3).

Therefore, the integer 27 can be written as the product of the perfect square 9 and the integer 3, which is 9 x 3.

Answer:

c.

Step-by-step explanation:

[tex]\frac{5}{4}+\frac{7}{9} = \frac{5*9+7*4}{4*9} = \frac{45+28}{36} = \frac{73}{36}[/tex]

and [tex]\frac{73}{36}= 2(36) + 1 = 2\frac{1}{36}[/tex]

Answer:

Option 4 - domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Step-by-step explanation:

Given :  [tex]h(x)=(0.5)^x-9[/tex]

To find : What are the domain, range, and asymptote of h(x) ?

Solution :  

Domain of the function is where the function is defined

The given function  [tex]h(x)=(0.5)^x-9[/tex] is an exponential function

So, the domain of the function is,

[tex]D=(-\infty,\infty) , x|x\in \mathbb{R}[/tex]

i.e, The set of all real numbers.

Range is the set of value that corresponds to the domain.

Let  [tex]y=(0.5)^x-9[/tex]

If [tex]x\rightarrow \infty , y\rightarrow -9[/tex]

If [tex]x\rightarrow -\infty , y\rightarrow \infty[/tex]

So, The range of the function is

[tex]R=(-9,\infty) , y|y>-9[/tex]

The asymptote of the function,

Exponential functions have a horizontal asymptote.

The equation of the horizontal asymptote is  when

[tex]x\rightarrow \infty[/tex]

[tex]y=(0.5)^\infty-9[/tex]

[tex]y=-9[/tex]

Therefore, Option 4 is correct.

Domain: {x | x is a real number}; range: {y | y > –9}; asymptote: y = –9

Answer:

For number 2:

Step-by-step explanation:

The fraction 1/50 is equivalent to 0.02 as a decimal.

To convert 1/50 to a percent, we multiply the fraction by 100:

= 1/50 x 100

= 2%

Therefore, 1/50 is equivalent to 2% as a percent.

To convert 1/50 to a decimal, we divide the numerator (1) by the denominator (50):

= 1 ÷ 50

= 0.02

Therefore, 1/50 is equivalent to 0.02 as a decimal.

Learn more about Decimal here:

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The corresponding reference angle to 17π/7 radians is π/7.

The corresponding reference angle to 17π/7 radians is found by determining the smallest positive angle such that when added to 17π/7 radians, the resulting angle lies between 0 and 2π radians.

To find the reference angle, we can subtract 2π radians repeatedly until we obtain an angle between 0 and 2π radians.

In this case, we have:

17π/7 - 2π = π/7

Therefore, the corresponding reference angle to 17π/7 is π/7 radians.

z = (x - 500) / 100

1.75 = (x - 500) / 100

175 = x - 500

675 = x

Answer:

A, 675

Step-by-step explanation:

Answer:

Step-by-step explanation:

First, add 9 to each side

Then subtract 2x from each side

Divide each side by 3

Sorry my answer may be a bit late

The rate at which the radius of the balloon is changing can be found by differentiating the volume formula for a sphere. Substituting the given values into the formula, we can calculate the rate of change at specific radii.

To find the rate at which the radius of the balloon is changing, we can use the relationship between the volume and the radius of a sphere. The volume of a sphere is given by the formula V = (4/3)πr³, where V is the volume and r is the radius. Taking the derivative of both sides with respect to time, we get dV/dt = 4πr²(dr/dt). We are given that dV/dt = 900 cm³/min and we need to find dr/dt when r = 40 cm and r = 90 cm.

(a) Plug in the values into the formula: 900 = 4π(40)²(dr/dt). Solve for dr/dt: dr/dt = 900/(4π(40)²) ≈ 0.178 cm/min.

(b) Repeat the same steps for r = 90 cm: 900 = 4π(90)²(dr/dt). Solve for dr/dt: dr/dt = 900/(4π(90)²) ≈ 0.020 cm/min.

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The measurement of length and distance in mathematics, including the SI unit meter, different units, and measurement systems.

Measurement of Length, Width, Height, and Distance

Length is the measurement of the extent along the greatest dimension. The SI unit of length is the meter (m). Units of length include kilometers (km), millimeters, and micrometers.

Distance is a quantity arrived at by measurements with material or optical apparatus. It is commonly measured in meters, kilometers, feet, yards, etc. in various systems of measurement.

Customary and Metric Systems are two different systems used for measuring length and distance.

Answer:

Total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .    

Step-by-step explanation:

As given

Zinnia and Ruby earn $58 per week for delivering pizzas.

Zinnia worked for x weeks and earned an additional total bonus of $13.

Ruby worked for y weeks.

Thus

Money Zinnia earns = Money earns per week × Number of weeks + Additional total bonus .

Put all the values in the above

Money Zinnia earns = 58 × x + 13

Money Zinnia earns = 58x + 13

Thus

Money  Ruby earns = Money earns per week × Number of weeks

Put all the values in the above

Money  Ruby earns = 58 × y

Money Ruby earns = = 58y

Thus

Total Zinnia and Ruby earned for delivering pizzas = Money Zinnia earns  + Money Ruby earns

Total Zinnia and Ruby earned for delivering pizzas = 58x + 13  + 58y

Therefore the total money Zinnia and Ruby earned for delivering pizzas is 58x + 13 + 58y .                          

Convert the line equation to 'y = mx + c' form. We calculate the orthogonal distance from the point to a generic point on the line using the formula 'd = |Ax1 + By1 + C| / sqrt(A^2 + B^2)'. Solve the line equation for 'y' using the computed 'd'. This yields the point closest to (-3,1) on the line.

The subject of the question involves the algebra of straight lines, specifically finding points on lines. The given line in the question is '6x + y = 9'. We want to find the point along this line that is closest to a given point (-3,1).

First, rewrite the equation in slope-intercept form: y = -6x + 9. Now recall the formula for the shortest distance from a point to a line, d = |Ax1 + By1 + C| / sqrt(A^2 + B^2), where 'A', 'B' and 'C' are the coefficients in the equation of the line, and '(x1, y1)' is the point.

In this case, A = -6, B = 1, C = -9, and the point is (-3,1). If we plug these into the formula, we can solve for 'd'. Then we solve the given equation for 'y' using the resulting 'd' value and we get the point which is closest to (-3,1) on the line '6x + y = 9'.

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The equation of a line parallel to y=23x+1 that passes through the point (-5, -2) is y = 23x + 113.

The subject of this question is geometry, specifically, the formulation of a linear equation. You're asked to write an equation of a line that passes through point (-5,-2) and is parallel to the line defined by the equation y=23x+1.

Parallel lines have the same slope, so since the given line has a slope of 23, our line will also have a slope of 23. The general form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. Here, 'm' is already known as 23. So, our equation currently is y = 23x + b.

We can determine 'b' using the given point (-5,-2). Substituting these coordinates into our equation gives -2 = 23*(-5) + b. Solving for 'b' renders b = -2 - (23*-5) = 113.

Therefore, the equation of the line that passes through (-5, -2) and is parallel to y=23x+1 is y = 23x + 113.

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